Access the full text.
Sign up today, get DeepDyve free for 14 days.
R. Brady (1971)
The consistency of the axioms of abstraction and extensionality in a three-valued logicNotre Dame J. Formal Log., 12
R. Sylvan, R. Brady (2005)
Relevant Logics and Their Rivals, Volume II
F. Drake (1974)
Set theory : an introduction to large cardinals
K. Kunen (1983)
Set theory - an introduction to independence proofs, 102
R. Routley, V. Plumwood, R. Meyer, R. Brady (1982)
Relevant logics and their rivals
Wilfrid Hodges (1980)
BASIC SET THEORYBulletin of The London Mathematical Society, 12
(1967)
Investigations in the foundations of set theory
(1989)
The non-triviality of extensional dialectical set theory
U. Petersen (2000)
Logic Without Contraction as Based on Inclusion and Unrestricted AbstractionStudia Logica, 64
J. Béziau (2011)
Universal logic : an anthology : from Paul Hertz to Dov Gabbay
Thierry Libert (2005)
Models for a paraconsistent set theoryJ. Appl. Log., 3
G. Wilmers (1989)
CANTORIAN SET THEORY AND LIMITATION OF SIZE: (Oxford Logic Guides 10)Bulletin of The London Mathematical Society, 21
C. Asmus (2009)
Restricted ArrowJournal of Philosophical Logic, 38
Michael Hallett (1984)
Cantorian set theory and limitation of size
Krzysztof Grabczewski (2001)
Equivalents of the axiom of choice
D. Batens (2000)
Frontiers of Paraconsistent Logic
J. Beall, R. Brady, A. Hazen, G. Priest, Greg Restall (2006)
Relevant Restricted QuantificationJournal of Philosophical Logic, 35
R. Meyer, R. Routley, J. Dunn (1979)
Curry's paradoxAnalysis, 39
(2000)
Paraconsistent mathematics
J. Ferreirós (2004)
From Frege to Gödel. A Source Book in Mathematical Logic, 1879¿1931: By Jean van Heijenoort. Cambridge, MA (Harvard University Press). 1967; new paperback edn., 2002. 664 pages, 1 halftone. ISBN: 0-674-32449-8. $27.95Historia Mathematica, 31
Greg Restall (1992)
A Note on Naive Set Theory in LPNotre Dame J. Formal Log., 33
R. Routley, Maureen Eckert (1983)
Exploring Meinong's Jungle and BeyondThe Journal of Philosophy, 80
Much thanks to Graham Priest
Lorenzo Peña (1990)
Paraconsistent logic: essays on the inconsistent
Z. Weber (2010)
Extensionality and Restriction in Naive Set TheoryStudia Logica, 94
J. Heijenoort (1967)
From Frege to Gödel: A Source Book in Mathematical Logic, 1879-1931
G. Priest (1987)
In Contradiction: A Study of the Transconsistent
R. Routley, R. Meyer (1976)
Dialectical logic, classical logic, and the consistency of the worldStudies in Soviet Thought, 16
This paper begins an axiomatic development of naive set theory—the consequences of a full comprehension principle—in a paraconsistent logic. Results divide into two sorts. There is classical recapture, where the main theorems of ordinal and Peano arithmetic are proved, showing that naive set theory can provide a foundation for standard mathematics. Then there are major extensions, including proofs of the famous paradoxes and the axiom of choice (in the form of the well-ordering principle). At the end I indicate how later developments of cardinal numbers will lead to Cantor’s theorem, the existence of large cardinals, and a counterexample to the continuum hypothesis.
The Review of Symbolic Logic – Cambridge University Press
Published: Jan 14, 2010
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.